Sharp bounds for psi function

DOI10.1016/j.amc.2015.07.012zbMath1410.33012OpenAlexW947659417MaRDI QIDQ668225

Xiao-Hui Zhang, Yu-Ming Chu, Zhen-Hang Yang

Publication date: 18 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.07.012

zbMATH Keywords

monotonicitygamma functionpsi function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Inequalities involving other types of functions (26D07)

Related Items (18)

Windschitl type approximation formulas for the gamma function ⋮ The monotonicity and convexity of a function involving psi function with applications ⋮ Monotonicity rules for the ratio of two Laplace transforms with applications ⋮ Improvements of the bounds for Ramanujan constant function ⋮ Fast convergence of generalized detemple sequences and the relation to the Riemann zeta function ⋮ Monotonicity and sharp inequalities related to gamma function ⋮ On rational bounds for the gamma function ⋮ A positive answer to Bhatia-Li conjecture on the monotonicity for a new mean in its parameter ⋮ Some new inequalities of Hermite-Hadamard type for \(s\)-convex functions with applications ⋮ Landen inequalities for a class of hypergeometric functions with applications ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ New properties of the divided difference of psi and polygamma functions ⋮ Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind ⋮ Notes on three conjectures involving the digamma and generalized digamma functions ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions ⋮ Complete monotonicity and inequalities related to generalized \(k\)-gamma and \(k\)-polygamma functions ⋮ New properties for the Ramanujan \(R\)-function

Cites Work

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• Monotonicity properties of functions related to the psi function
• On some properties of digamma and polygamma functions
• Inequalities for the gamma function
• New approximations of the gamma function in terms of the digamma function
• Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions
• Monotonicity properties of the gamma function
• Accurate Estimates of the Gamma Function Involving the PSI Function
• Monotonicity of some functions involving the gamma and psi functions
• Sharp bounds for the psi function and harmonic numbers
• Some properties of the psi and polygamma functions
• Sharp inequalities for the digamma and polygamma functions
• INEQUALITIES INVOLVING GAMMA AND PSI FUNCTIONS
• On some properties of the Gamma function
• Some properties of the gamma and psi functions, with applications

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